I have a book which claims that the Neandertal facial morphology could
be caused by environmental effects, rather than being genetic in origin.
As support, it quotes the following paragraphs from Klein's "The Human
Career":

The full functional interpretation of Neanderthal facial structure is a
matter of ongoing debate, but there are some points of broad agreement.
The forward placement of Neanderthal jaws and the large size of the
incisors probably reflect habitual use of the anterior dentition as a
tool, perhaps mostly as a clamp or vise. Such para- or nonmasticatory
use for gripping is implied by the high frequency of enamel chipping and
microfractures on Neanderthal incisors, by nondietary microscopic
striations on incisor crowns, and by the peculiar, rounded wear seen on
the incisors of elderly individuals. Similar, though less extensive
damage occurs on the teeth of Eskimos, who also tend to use their
anterior jaws extensively as clamps.

Biomechanically, the forces exerted by persistent, habitual,
nonmasticatory use of the front teeth (= "massive anterior dental
loading") could account in whole or in part for such well-known
Neanderthal features as the long face, the well-developed supraorbital
torus, and even the long, low shape of the cranium. Massive anterior
dental loading could further explain the unique Neanderthal
occipito-mastoid region which perhaps provided the insertions for
muscles that stabilized the mandible and head during dental clamping.

Now, I would have interpreted that to mean that Neandertals evolved
facial features to handle the stresses of using teeth and jaws for
non-eating purposes. But Klein's wording is vague enough (especially in
the first sentence, second paragraph) that I can't rule out the
alternative explanation that dental loading could directly cause these
facial features in an individual with no genetic predisposition towards
them.